Physics and Measurement
CHAPTER OUTLINE
1.1 Standards of Length, Mass, and
Time
1.2 Matter and Model-Building
1.3 Dimensional Analysis
1.4 Conversion of Units
1.5 Estimates and Order-of-
Magnitude Calculations
1.6 Signifi cant Figures
ANSWERS TO QUESTIONS
* An asterisk indicates an item new to this edition.
Q1.1 Density varies with temperature and pressure. It would
be necessary to measure both mass and volume very
accurately in order to use the density of water as a
standard.
Q1.2 (a) 0.3 millimeters (b) 50 microseconds
(c) 7.2 kilograms
*Q1.3 The answer is yes for (a), (c), and (f ). You cannot add or
subtract a number of apples and a number of jokes. The
answer is no for (b), (d), and (e). Consider the gauge of a
sausage, 4 kg2 m, or the volume of a cube, (2 m)3. Thus
we have (a) yes (b) no (c) yes (d) no (e) no (f ) yes
Q1.4 No: A dimensionally correct equation need not be true. Example: 1 chimpanzee = 2 chimpanzee
is dimensionally correct.
Yes: If an equation is not dimensionally correct, it cannot be correct.
*Q1.5 The meterstick measurement, (a), and (b) can all be 4.31 cm. The meterstick measurement and
(c) can both be 4.24 cm. Only (d) does not overlap. Thus (a) (b) and (c) all agree with the
meterstick measurement.
*Q1.6 41 € ≈ 41 € (1 L1.3 €)(1 qt1 L)(1 gal4 qt) ≈ (101.3) gal ≈ 8 gallons, answer (c)
1
SOLUTIONS TO PROBLEMS
Section 1.1 Standards of Length, Mass, and Time
P1.1 Modeling the Earth as a sphere, we fi nd its volume as
4
3
4
3
6 37 10 πr3= π(. × 6m)3=1.08×1021m3.
Its density is thenρ= = ×
×
= × m
V
5 98 10
1 08 10
5 52 10
24
21 3
3 3 .
.
.
kg
m
kg m . This value is intermediate
between the tabulated densities of aluminum and iron. Typical rocks have densities around 2 000
to 3 000 kgm3. The average density of the Earth is signifi cantly higher, so higher-density material
must be down below the surface.